Question

18) Write the relation between 0, P(E) and 1.​

Answer 1

SOLUTION :

TO DETERMINE

The relation between 0, P(E) and 1

Where P (E) is the probability of an event E

EVALUATION

In any random experiment if the total number of elementary (Simple) events in the sample space be n ( A finite number ) among which the number of elementary events favourable to an event E, connected with that experiment, be m then the probability of E, denoted by P(E), is defined as

$\displaystyle \sf{ \: }P(E) = \frac{m}{n}$

Here it is obvious that

$\sf{0 \leqslant m \leqslant n}$

$\implies \displaystyle \sf{ \: }0 \leqslant \frac{m}{n} \leqslant 1$

$\therefore \: \displaystyle \sf{ \: }0 \leqslant P(E) \leqslant 1$

Which is the required relation between 0, P(E) and 1

ADDITIONAL INFORMATION

1. For a certain event S, all the cases are favorable cases so that P( S ) = 1

2. For an impossible event O the number of favorable cases is zero so that P(O) = 0

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